已知|2x-y|=3,求8x^2-8xy+2y^2-8x+4y-6
问题描述：
已知|2x-y|=3,求8x^2-8xy+2y^2-8x+4y-6
答
|2x-y|=3,(2x-y)^2=9,2(2x-y)^2=18,
即 8x^2-8xy+2y^2=18,
则 f(x,y) = 8x^2-8xy+2y^2-8x+4y-6 = 12-8x-4y =12-4(2x-y)= 12-4(±3),
则 f(x,y)=0 或 f(x,y) = 24